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What is the solution to the differential equation dy/dx = 3x^2?

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Question: What is the solution to the differential equation dy/dx = 3x^2?

Options:

  1. x^3 + C
  2. 3x^3 + C
  3. x^2 + C
  4. 3x^2 + C

Correct Answer: x^3 + C

Solution: 

Integrating both sides gives y = x^3 + C, where C is the constant of integration.

What is the solution to the differential equation dy/dx = 3x^2?

Practice Questions

Q1
What is the solution to the differential equation dy/dx = 3x^2?
  1. x^3 + C
  2. 3x^3 + C
  3. x^2 + C
  4. 3x^2 + C

Questions & Step-by-Step Solutions

What is the solution to the differential equation dy/dx = 3x^2?
  • Step 1: Start with the differential equation dy/dx = 3x^2.
  • Step 2: To find y, we need to integrate both sides of the equation with respect to x.
  • Step 3: Integrate the right side: ∫3x^2 dx.
  • Step 4: The integral of 3x^2 is x^3 + C, where C is the constant of integration.
  • Step 5: Therefore, the solution to the differential equation is y = x^3 + C.
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